A Reexamination of Inflation and Growth

Transcription

1 A Reexamination of Inflation and Growth Benjamin Lidofsky May 13, 2013 Abstract I rely on the empirical model created by Pollin and Zhu (2006) to examine the relationship between inflation and growth beyond the short-term. I replicate their set of countries and extend the period of time examined to I cannot duplicate their results and find that extensive data revisions may be a key reason for the discrepancy. I test slight adjustments of their model to reduce omitted variable bias. The enhanced model can be directly compared with the empirical work of Mankiw, Romer, and Weil (1992), allowing a contrast of my findings with one of the literature s foundations. The combination of the Pollin and Zhu and Mankiw, Romer, and Weil empirical models leads to increased explanatory power and more reliable estimates. From the combined model, there are indications of significant impacts of inflation on growth in the mediumterm (over five years), but negligible impacts over the long-term (twenty-five years). This is most evident in highly developed countries; the relationship between inflation and growth in less developed countries is less clear. 1 Introduction The 2007 financial crisis and subsequent global recession have increased the interest in determining what makes economies grow. Over the past few years, fiscal policymakers have debated the relative merits of Keynesian stimulus versus austerity, while monetary policymakers have similarly considered the benefits of low interest rate environments over stable I thank Professors Gibson, Mickey, and Sicotte, among others, for their support and advice on this endeavor. All remaining errors are my own. 1

2 prices. There are two main points of contention across these debates: are stimulative policies actually effective in rebalancing the economy and are the inflationary risks associated with those measures so costly that they nullify any potential benefits? Particularly regarding monetary policy, this latter question has become increasingly critical as economies experience stronger recoveries. To seek to answer either of these questions with one study is to ask a lot of the data. This study takes a more focused approach and examines the relationship between inflation and growth over the medium- and long-term. The remainder of this paper is divided into five sections. Section 2 provides a summary of the literature, Section 3 describes the methodology, Section 4 examines the results, Section 5 discusses the implications of the findings, and Section 6 concludes. 2 Literature Review This section examines two topics: general growth models and empirical studies on the relationship between inflation and growth. 2.1 Growth Models The Solow (1956) growth model represents one of the foundational components of neoclassical economics. It expands the Harrod-Domar model by relaxing the assumption that factors of production are used in fixed proportions. Instead, Solow allows for labor and capital to be substituted for one another. This stabilizes the equilibrium condition for long-term growth, which was previously precariously balanced on a knife-edge, as Solow characterizes it. In the Harrod-Domar model, even slight deviations in the components of growth (such as an increase in the savings rate) lead to an unstable path for per capita 2

3 income. With Solow s model, steady-state per capita output is determined by the economywide savings rate and the growth rate of population, both of which are exogenously given. A higher savings rate, ceteris paribus, 1 means that investment is higher, leading to an increase in the level of capital, which boosts output in the steady state. Conversely, faster population growth, ceteris paribus, lowers the stock of capital per worker, making labor less productive. This undermines growth in the steady state. As an extension to his basic model, Solow also incorporates exogenous technological change into the framework. Technology enhances the productivity of capital or labor, thereby leading to higher levels of output. While Solow notes that there are numerous ways in which technology can be introduced into his model, he focuses on exogenous, neutral changes in technology, which act as a simple multiplier to the initial output of capital and labor. Assuming a Cobb-Douglas production function, 2 in which there are diminishing marginal returns on factors of production, the Solow steady state level of per capita output can be characterized by ln[ Y (t) ] = lna(0) + gt + α L(t) 1 α ln(s) α ln(n + g + δ) (1) 1 α where Y (t) is the level of output at time t, L(t) is the stock of labor at time t, A(0) is the initial stock of technology, g is the growth rate of technology, α is the marginal return on capital, s is the savings rate, n is the rate of population growth, and δ is the rate of capital depreciation. Mankiw, Romer, and Weil (1992) expand on Solow s (1956) model by factoring in human capital, a broad term that includes workers education, experience, and other forms of 1 Latin for all else equal, meaning that only the variable in question changes value. 2 The Solow model itself is general enough to allow for other specifications. However, it is convenient to focus specifically on the Cobb-Douglas function here, as it is particularly relevant to the later discussion of Mankiw, Romer, and Weil (1992). 3

4 knowledge. They note that human capital has long held a predominant role in economic theory and that its exclusion may bias the estimated parameters of the other variables in empirical replications of the Solow model. To support their belief, Mankiw, Romer, and Weil observe that the majority of capital stock in the United States was in the form of human, rather than physical, capital in 1969 (Kendrick, 1976, via Mankiw, Romer, and Weil, 1992). As such, the inclusion of human capital to the model may lead to important adjustments to the original Solow model. Mankiw, Romer, and Weil introduce human capital to the theoretical model by including it as a factor of production. The model is now represented by Y (t) = K(t) α H(t) β [A(t)L(t)] 1 α β (2) where K(t) is the stock of physical capital at time t, H(t) is the stock of human capital at time t, and β represents the marginal return on human capital. Including human capital yields the following equation for per capita output in the steady state ln[ Y (t) ] = lna(0) + gt α L(t) + β 1 α β ln(n + g + δ) + α 1 α β ln(s k) + β 1 α β ln(s h) (3) where s k represents the share of income invested in physical capital and s h represents the share of income invested in human capital. In their 1992 study, Mankiw, Romer, and Weil also run regressions on a sample of countries to determine the effectiveness of their augmented Solow model. Their dependent variable is the log difference in output per working-age person from 1960 to 1985 (i.e., the difference between the values in the two years, not the average annual growth rate during the period). In their representation of the Solow (1956) model, the initial log level of gross domestic product (GDP) is used to approximate the initial stock of technology, lna(0) (from equation 3) and the logged savings rate accounts for ln(s k ). Depreciation and technological change are assumed to be constant across countries and time, so these assumed values are 4

5 added to the population growth rate and the log value of this is taken, which incorporates ln(n + g + δ) into the regressions. They find that the inclusion of a proxy variable for human capital (ln(s h ) in equation 3) the log value of the average share of the working age population attending secondary school significantly enhances the overall descriptive power of their regression model and alters the coefficients on all of the other variables. This suggests that Mankiw, Romer, and Weil had eliminated some omitted variable bias. The initial presence of omitted variable bias may explain why, in their regressions to test the original Solow model, Mankiw s, Romer s, and Weil s calculated parameters do not support what the theoretical model would suggest. However, with the inclusion of the human capital proxy, the other coefficients are more consistent with the theoretical model. As theirs is an augmented version of the Solow model, the conclusions of Mankiw, Romer, and Weil (1992) do not wholly confirm Solow s findings. For example, Mankiw, Romer, and Weil find that the savings rate plays a more significant role in determining the level of per capita output in the steady state than previously thought and that the inclusion of human capital makes the growth rate of population more significant. In particular, given a higher population growth rate, the stock of human capital must be distributed across more workers, which, in turn, lowers labor productivity. This is similar to population growth s impact on the distribution of physical capital across the labor force. An additional finding of the 1992 study is that the augmented Solow model estimates that it takes an economy roughly twice as long to achieve half of its steady state as the original Solow model would suggest. Both the initial and augmented Solow models, as is common in exogenous growth theory, focus on the economy at the steady state. As used in Solow (1956) and in Mankiw, Romer, and Weil (1992), the steady state refers to the environment in which per capita output does not change over time, as capital per worker becomes constant. The overall stock of 5

6 capital increases, but only to keep up with population growth and depreciation. Given Keynes famed quote of how, in the long run, we are all dead, the relevance of the steady state to the present-day economy may be questioned. Further, other growth models have found that an economy can grow in perpetuity without reaching a steady state. Endogenous growth theorists, for example, believe that the returns on factors of production do not necessarily need to be diminishing and, therefore, an economy can expand indefinitely. Such theories tend to aggregate up from microeconomic behavior, which contrasts from Solow s examination of broad, exogenously determined characteristics. For example, Lucas (1988) establishes a learning-by-doing model in which a country s initial level of capital is a key determinant of its long-term growth. Bernanke and Gürkaynak (2002) find the empirical framework of Mankiw, Romer, and Weil (1992) to be sufficiently flexible to test various theoretical growth models and their results suggest that there is some endogeneity in growth. Bernanke s and Gürkaynak s ability to use the Mankiw, Romer, and Weil regression model to examine various conceptions of growth suggests that the model may be of use for this study, as well. Implicit in the models above is the belief that, at equilibrium, the economy is operating at full capacity. This is a hallmark of classical and neoclassical economics; economies achieve equilibrium at one level of output. Keynesian theory relaxes this assumption and allows for involuntary unemployment to be a persistent trait of the economy. Involuntary unemployment occurs when there is insufficient demand for employees McConnell, Brue, and Flynn (2012). Such unemployment may be inelastic relative to wages, meaning that normal market forces cannot effectively bring the economy back to full employment output. The implications of this are that prolonged stagnation may occur, undermining the economy s trajectory towards the steady-state. Unlike Solow (1956) and other neoclassical models, Keynesian economics focuses on invest- 6

7 ment spending, rather than on savings, as a key determinant of growth. Keynes believed that investment was one of the most unreliable components of growth (Meltzer, 1988). In particular, it was very unlikely for there to be equilibrium in the loanable funds market. The reasons for this are largely due to Keynes reliance on future expectations as a determinant of the level of investment. Not all income has to be consumed or saved; some of it can be hoarded for what Keynes (1937) refers to as liquidity-preference. Economic agents do not have perfect information; the future is, at least to a certain extent, uncertain. Liquidity-preference provides insurance against this uncertainty. However, this hoarded money cannot be used for investment, which undermines growth. Liquidity-preference is not the only way in which uncertainty enters the loanable funds market. Investment is directly impacted as well. In addition to the future being inherently difficult to predict, another form of risk highlighted by Keynes is the potential for losses due to the failure of an investment project (Meltzer, 1988). Businesses must consider future revenues in order to properly determine whether they should invest; the more ambitious the project, the more certain the firm must be in order to be willing to invest. Expectations of future trends are likely to be based on current conditions; as such, investment spending tends to be diminished during economic contractions. This undermines the economy s ability to return to full employment equilibrium. This is where one of the quintessential aspects of Keynesian economics, a key role for the government, becomes prominent. The government does not need to make its investment or spending decisions based on expectations of the future; it can act counter-cyclically. When the private sector curbs its spending due to pessimism regarding the future, the government can step in to counter this. Ideally, this can help the economy both maintain equilibrium and operate at full employment output. However, it presumes that the government is able to calculate the precise amount of spending needed to obtain this level of output. Friedman 7

8 (1968), among others, has provided numerous reasons why this does not happen in practice. Friedman, for example, has observed that policymakers have a tendency to not wait for their stimulus to take effect. As a result, they often employ additional rounds of stimulus in order to achieve the desired effect. This over-stimulus undermines the economy s ability to recover by excessively growing the money base and crowding out private investment. Another downside of the Keynesian approach is that it does not have a testable model for the economy. While Solow (1956) is able to distill the steady-state economy into a handful of equations, Keynes has nothing comparable. This makes it difficult to test the implications of Keynesian theory to the same extent that Mankiw, Romer, and Weil (1992) were able to do with the Solow model. To account for this, many researchers have used Keynesian economics as a guide rather than as a formula, per se. Keynes presents numerous reasons why an economy may not operate at full employment output. Researchers can include a variety of variables to proxy Keynes reasons. I have taken the time here to briefly discuss these different approaches, as I believe it is critical to understand the underpinning theories that determine the empirical models used in the literature. The variables, time frames, and countries employed should all reflect different aspects of the theoretical literature on growth. In particular, an empirical model based on neoclassical growth theory makes different assumptions than a model informed by Keynesian theory. It is important to be able to recognize these assumptions. 2.2 Empirical Studies Regarding Inflation and Growth One of the persistent traits to come from the empirical literature on inflation and growth is that the two variables appear to have a nonlinear relationship. In general, extreme rates of inflation have been found to have the most detrimental impacts on growth. The primary 8

9 question posed by the literature is whether the relationship is significant across all levels of inflation. Is there a range of inflation rates at which inflation is costless to growth? The point at which the relationship between inflation and growth becomes significant is referred to as the threshold. This discussion will largely concentrate on panel studies running linear regressions, though some analyses have used other methods, such as the instrumented variables approach taken by Vaona (2012). Overall, the results have been mixed. Gordon (2011) notes that the inflation-growth relationship may vary over time; studies of the period between 1973 and 1981 suggest that supply shocks played a predominant role. In particular, price-inelastic demand for goods and services allowed for shocks to impact the price level over the shortterm. Bruno (1995) comes to a similar conclusion, noting a positive association between inflation and growth during the 1960s, but a negative one in subsequent decades. Additionally, Ball and Mankiw (1995) suggest that relative price changes may have more significant impacts on growth than do aggregate price changes. Bruno and Easterly (1998) and Motley (1998) find that when the length of the time period examined is expanded, the statistical significance of the relationship between inflation and growth tends to weaken. However, Andrés and Hernando (1999) determine that a longterm, negative relationship exists across all levels of inflation. Other studies estimate the threshold of significance to be quite low; Ghosh and Phillips (1998), for example, calculate a rate around 2.5 percent. However, other studies find the threshold to be around 10 percent (e.g., Judson and Orphanides, 1999; Burdekin et al., 2004). Burdekin et al. (2004) raise concerns over whether some threshold estimates may be biased by not properly accounting for multiple breaks in the inflation-growth relationship; their study finds evidence that as many as four exist. Some studies, such as Fischer (1993), have not focused on determining a threshold, but a turning point the growth-maximizing rate of inflation. A caveat to the 9

10 precision of these findings comes from Bruno and Easterly (1998), who find that outlier observations, particularly cases of hyperinflation, are the predominant determinant of their findings. An additional focus of this branch of the literature has been on examining countries of varying levels of economic development. Studies that focus solely on countries with highly developed economies tend to find a significant, negative association between inflation and growth (e.g., Andrés and Hernando, 1999). When a broader spectrum of countries is examined, though, the significance diminishes (e.g., Barro, 1996; Pollin and Zhu, 2006). Burdekin et al. (2004) suggest, however, that examining countries at various levels of development at the same time may lead to spurious results. When countries are examined separately by level of development, less developed countries seem to have higher inflationary thresholds than more developed countries (e.g., Pollin and Zhu, 2006). This suggests that developing countries can tolerate a higher level of inflation without undermining their growth. 3 Methodology This section contains four parts. First, the hypothesis is stated and briefly discussed. Next, the statistical framework used to examine the data is described. The variables chosen for the model are then detailed. Lastly, concerns of the validity of the model are discussed. 10

11 3.1 Hypothesis This study tests for the presence of a statistically significant relationship between inflation and output growth over time, with a particular emphasis on longer trends. In particular, this relationship is anticipated to be nonlinear and associated with a non-negative growthmaximizing rate of inflation. It is further assumed that, as longer periods of time are examined, the relationship between inflation and growth will diminish in significance. Joint hypothesis tests will determine if the inflation variables included all have true coefficients of zero. Further, it may be possible to make inferences on the growth-maximizing rate of inflation if the inflation variables are statistically significant. 3.2 Statistical Framework The methodology of this paper is linear regression. Following Pollin and Zhu (2006), I use two separate specifications for the regression model: ordinary least squares (OLS) and fixed effects (FE). Regression analysis seeks to find an intercept and set of slope coefficients that minimizes the sum of squared error from the data to the estimated regression plane. Algebraically, this is represented as Ŷ i = ˆβ 0 + ˆβ X i (4) where Ŷi represents the estimated value of the dependent variable, Y i for the i th observation, ˆβ 0 represents the constant, ˆβ represents the estimated vector of coefficients associated with X i, the vector of independent variables whose values correspond to the i th observation. The true vector of coefficients is β. The OLS regression determines the linear combination that minimizes the sum of the squared distance between Ŷi and Y i. The Gauss-Markov theorem states that, based on assumptions discussed below, OLS estimates have the least variance of all possible linear estimates of Y (Stock and Watson, 2011). For this reason, the use 11

12 of OLS and associated regression forms provides the best linear approximation of the true relationships between the independent variables and the dependent variable. In using OLS regressions, several assumptions about the data must be made. In particular, Independent variables are fixed in repeated samples and are uncorrelated with the error term. The expected value of the error is zero and has finite kurtosis. This also implies that the expected value of the estimate of the dependent variable is the true value of the dependent variable. The errors are independently and identically distributed between different observations. Lind, Marchal, and Wathen (2008) note that this assumption may not hold for time series analysis, which is of particular concern to this study. An additional assumption often made with OLS regressions is that the error is homoskedastically distributed that is, the distribution of the error is not expected to vary based on the level of the dependent variable. If this is not the case, and the error is heteroskediastically distributed, it is inappropriate to use conventional standard errors. Stock and Watson (2011) recommend the use of clustered standard errors when using panel data, as this specification is able to account for both heteroskedasticity and serial correlation in the error. In particular, clustered standard errors control for potential correlations within groups (Baum, 2006). Here, standard errors will be clustered about countries. As this study uses panel data, alternative regression models can also be used. Panel data, or pooled cross sectional times series, are used to track the same entities (e.g., countries) across time (e.g., years). This structure allows for the mitigation of potential bias caused by variables outside of the set of independent variables. If such variables are correlated 12

13 with both the dependent variable and one of the control variables, the control variable has omitted variable bias. This bias makes the estimated coefficient of the control variable unreliable, as it is skewed by the exclusion of the omitted variables. To minimize potential sources of omitted variable bias, three different strategies are undertaken. First, time period dummy variables are included in all regressions, as done in Pollin and Zhu (2006). These dummy variables are able to account for potential omitted variables that are constant across entities, but vary over time. Additionally, like Pollin and Zhu (2006), regressions are estimated both with OLS and with fixed effects (FE). FE regressions control for omitted variables that vary across entities, but are constant over time. The FE regression model is described in detail below. The last way in which omitted variable bias is countered is by critically examining the independent variables used and determining if alterations may be made to reduce the risk of such bias. While omitted variable bias may affect any of the independent variables, the particular concern here is on how the bias may impact the inflation coefficients. FE regressions assume that there are inherent characteristics of the individual entities in the dataset, which are not fully explained away by the set of independent variables. These characteristics are assumed to be constant over time and uncorrelated across entities. If these characteristics are not accounted for, the variables in the model have omitted variable bias. Notationally, these characteristics can be defined as the variable Z, where z i represents the characteristics of the i th entity. It is assumed that Z and the independent variables are correlated. To mitigate this bias, the FE regression includes the parameter α, which is equal to β 0 + Z. Each element of α, α i will pick up all constant terms of the regression, in particular the characteristics inherent of the i th entity. Algebraically, this yields ˆ Y it = ˆβ X + α i + u it (5) 13

14 where i indexes across entities, t indexes across time, and u it is the residual associated with the particular observation. While the FE regression model is an improvement over OLS in its ability to control for these omitted variables, the manner in which it does this combines all constant terms in the regression. This prevents the inclusion of independent variables that are constant over time; variables which may be of interest in their own right (e.g., the initial level of GDP in the Mankiw, Romer, and Weil (1992) empirical Solow model). For this reason, both OLS and FE regressions are used in this study. 3.3 Variables Pollin and Zhu (2006) rely on panel data for 80 countries from 1961 to They run two sets of regressions, one on annual data to test for short-term effects, and one on five-year averages to test for medium-term effects. 3 Observations where the population is less than two million are excluded, based on the belief that those economies are not large enough to behave in a conventional manner (Pollin and Zhu, 2006). As the literature discussed above supports the assumption that the relationship between inflation and growth is nonlinear, Pollin and Zhu introduce two forms of nonlinearity into their model. First, observations where the inflation rate was greater than 40 percent are excluded from the dataset. This is in keeping with the results of Bruno and Easterly (1998), who found that their findings were being biased by outlier observations. Additionally, in order to determine whether nonlinearities are present below this 40 percent ceiling on inflation, the squared term of the inflation rate is included as an explanatory variable. This permits the turning point, the inflation rate that maximizes the output growth rate, to be calculated. The turning 3 Pollin and Zhu (2006) refer to the five-year average regressions as long-term effects, but this paper will refer to them as medium-term effects so as to distinguish them from the twenty-five year averages used in Mankiw, Romer, and Weil (1992). 14

15 point is calculated by taking the partial derivative of growth with respect to the inflation rate, and solving for the inflation rate. This results in the following: Inflation Coefficient Turning Point = 2 Inflation-Squared Coefficient (6) Pollin and Zhu (2006) include eleven variables in their regressions to estimate the growth rate of real per capita gross domestic product (GDP), as measured by the difference between logged values. I discuss each of the independent variables in turn in order to describe the environment in which Pollin and Zhu (2006) and this study examine inflation and to provide expected signs for the coefficients (i.e., positive, negative, or ambiguous). These expectations are determined by the literature. 1. The share of government consumption in GDP: High government consumption relative to GDP suggests that the private sector is not particularly robust. This undermines growth by limiting innovation. This can be particularly detrimental to growth in the long-run. During economic crises, though, fiscal stimulus may be effective in stabilizing and rebalancing the economy, thereby leading to higher growth. While the former observation is fairly universal across economic theories, the latter is particularly Keynesian in nature. Neoclassical economics suggests that fiscal stimulus is not an effective way to reverse a recession. For example, increased fiscal spending may crowd out investment, which discourages businesses from expanding. Further, even if fiscal stimulus does lead to stronger growth, its effects may only be observable with a time lag. Given these factors, I anticipate the sign of government consumption to be negative. 2. The government budget surplus as a percentage of GDP: A positive government surplus means that tax revenues exceed government expenditures. As such, the surplus will likely be negative (i.e., the country has a budget deficit) during economic 15

16 downturns due to a combination of weaker tax receipts, automatic stabilizers (government programs, such as unemployment insurance, that engage during a recession independently of government action), and potential attempts at fiscal stimulus. If governments run prolonged negative budget surpluses, they generally need to go into debt in order to sustain their spending. Government borrowing can crowd out private borrowing, thereby curbing investment and undermining economic growth. For these reasons, government budget surpluses should have a positive impact on growth. 3. The share of investment in GDP: High shares of investment in GDP lead to higher stocks of capital in the economy, which enhance labor productivity, promoting growth. Additionally, investment can lead to technological innovation, which also spurs growth. As such, higher levels of investment should have a positive impact on growth. 4. Initial level of per capita GDP: This is an indicator of a country s level of economic development at the beginning of the period. Convergence theory suggests that, upon achieving the steady state, all countries will be at the same level of per capita output. If this is true, high levels of per capita GDP will have a negative impact on growth, particularly in the long run. The evidence for such an effect has been mixed: some studies (e.g., Lucas, 1988) do not support convergence theory, though Mankiw, Romer, and Weil (1992) do find support for conditional convergence. Additionally, Barro (1996) uses a similar approach to that of Pollin and Zhu (2006) and finds the coefficient of initial per capita output to be negative. As such, the estimated coefficients for this variable are likely to be negative. 5. Life expectancy at birth: Long life expectancy suggests that individuals in the country have a high quality of life and, in particular, that they are healthy. This should lead to a more productive labor force and, therefore, to stronger growth. 16

17 Additionally, high life expectancy provides more opportunities to acquire human capital, and therefore may also enhance labor productivity through this channel as well. Therefore, life expectancy should be positively correlated with growth. 6. Average years of secondary schooling in the adult population: This is a proxy for the level of human capital in the labor force. A more educated labor force should be able to use more advanced technologies and is predisposed towards innovation. This should be particularly true over long periods of time. As such, education should be positively correlated with growth. 7. Change of terms of trade weighted by the sum of imports and exports as a percentage of GDP: There are two components to this variable. First, if the variable is positive in sign, it means that the country s terms of trade improved, either because exporters were able to profit more from their sales, consumers were able to import more cheaply, or some combination of the two. Because of this, the trade variable should be positively associated with growth. The second component of the variable is the exposure of the economy to foreign markets. Large values of this variable, positive or negative, indicate that trade represents a significant portion of the country s economy. The share of trade in the economy has no influence on the sign of the variable, because trade cannot be negative. However, this factor is important, because it will weight changes in terms of trade by their relevance to national output as a whole. 8. Share of population affected by natural disasters weighted by the share of agricultural output in GDP: Natural disasters can both ruin agricultural crops and destroy infrastructure, both of which restrict output. This destruction may take a considerable time to repair, meaning that natural disasters may have prolonged impacts on growth. Natural disasters are therefore likely to have a negative impact 17

18 on growth. 9. Participation in armed conflict with more than 25 deaths: Wars can exact horrific costs on an economy, both through the loss of lives and through the destruction of private property and public infrastructure. Additionally, firms are less likely to invest in war zones, as there are outsized risks that projects will be eradicated and consumer demand is unlikely to be strong. Pollin and Zhu (2006) assign three values to this variable: 1 if a war was recorded within the country s boundaries, -1 if the country participated in a war in another country, and 0 for all instances without war. This specification assumes that participation in foreign wars will have an equal and opposite effect of participation in domestic wars. As I believe that all wars will have negative impacts on growth, I find it difficult to speculate on an expected sign within this framework. Therefore, I regard the coefficient of this variable, given its specification, to be ambiguous in sign. 10. Inflation: Inflation shall be measured through the consumer price index. As I assume the threshold rate of inflation is non-negative (i.e., either zero or positive), I expect inflation to have the opposite sign of the squared inflation variable. As the model has multiple inputs, the standard second derivative test cannot be used to estimate the sign of the expected coefficient of inflation. For this reason, I classify it as ambiguous. 11. Squared Inflation: The preceding logic regarding inflation is equally relevant to squared inflation. As such, I expect squared inflation to have the opposite sign as inflation, in order for the threshold rate to be non-negative, but cannot make any inferences on what the sign would be. Therefore, the expected coefficient for squared inflation is ambiguous. 18

19 In addition to the variables listed above, time dummy variables are included in all of the regressions, to control for any potential omitted variable bias consistent across countries. It is not useful to speculate as to what sign these variables might have, as their importance lies not in their explanatory power, but in their ability to help better estimate the coefficients of the other variables. These dummy variables are only able to inform on what occurred in the past; what the coefficient for the 1970 dummy variable was provides little insight in what may occur in the future. The countries used in this analysis are listed in Appendix A. The sources used for and constructions of each variable are provided in Appendix B. 3.4 Model Validity There are two major forms of model validity: internal and external. If the model is internally valid, it is a reliable representation of reality. If the model is externally valid, then the results found here are relevant to populations and periods not included in the sample. I will discuss concerns of validity extensively, as I believe such issues are not sufficiently discussed in the literature. There are five major biases that may undermine the model s internal validity: omitted variable bias, misspecification of functional form, errors-in-variables bias, missing data and/or sample selection bias, and simultaneous casualty bias (Stock and Watson, 2011). Omitted variable bias is a predominant concern, as it skews the estimated coefficients and undermines attempts to make inferences. This study critically examines the approach taken by Pollin and Zhu (2006) to try to minimize the risk of omitted variable bias. A more detailed description of the alterations made is reserved for Section 4.3. Even with these model adjustments, there are certain potential causes of omitted 19

20 variable bias that are difficult to quantify. For example, Keynesian economics would assert that uncertainty regarding the future impacts growth, principally through investment. However, uncertainty cannot be easily measured and the data that do exist are not broadly available across countries or time. The time dummy variables and FE regressions may reduce this bias to a certain extent, if omitted variables are constant over either countries or time, but this study makes no claim that the risk of omitted variable bias has been wholly mitigated. Regarding functional form, Zarnowitz (1985) notes that many of the detriments of growth have nonlinear impacts. Despite this, the vast majority of the independent variables used here are represented linearly. The decision to rely predominately on linear relationships is based on several reasons. First, it is beyond the scope of this study to presume how the relationship between each variable and growth may be nonlinear does it follow a quadratic curve, a logarithmic progression, or some other path? To determine and test alternative structures for each control variable would be a very time consuming task and would take away from the focus on inflation. Additionally, nonlinearities are most likely to prevalent at the extremes. This assumption was already present in this study, as inflation rates beyond 40 percent are excluded. Between extreme values, I assume that a linear relationship exists between the independent variables and growth. In keeping with Pollin and Zhu (2006), as well as countless other studies, I assume that the linear specification of the majority of variables is appropriate. In a few instances, an additional concern regarding functional form is whether the variables chosen for this model are accurate representations of the phenomena they are supposed to depict. For example, the educational variable may not be an effective proxy of human capital. The specification here relies on the average years of secondary 20

21 school education in the adult population. Particularly in developed countries, this may not be a reasonable approximation of human capital; the average years of tertiary school education may be more valid. Levine and Renelt (1992) note as well that the use of schooling variables to approximate the stock of human capital may be ineffective, because such data do not account for relative variation in the quality of education. As such, two observations may have the same average years of schooling, but have different levels of knowledge. The data here are unable to account for this. Concerns of functional form bias may be legitimate. However, limitations in the availability of data prevent these issues from being completely addressed. Even so, it is reasonable to assume that the majority of the control variables used in this study have a linear relationship with growth over moderate values. Ultimately, the potential presence of functional form biases leads me to qualify the inferences made from the regression results. Errors-in-variables bias is another major concern for this study. The data used in this study are estimates; estimates which are prone to revision over time. In order to determine whether revisions in the data may be substantial enough to bias the results, I examine differences in the values of the dependent variable used in the regressions here from the values used in Pollin s and Zhu s. As can be seen in Figure 1, countries with higher levels of income tend to have smaller revisions. Lower income countries have large revisions at times. In fact, as shown in Table 1, there are nine instances where revisions were quite extensive and all of these occurred to low income countries. Clearly, these revisions are not negligible; in 2002, economists thought Haiti grew by 21.5 percent in Now the economy is estimated to have contracted by -9.4 percent. More importantly, these revisions are also nonrandom; for example, revisions in high-income countries tend to be smaller in absolute value than 21

22 those in lower-income ones. This indicates that the error present here is not classical measurement error, which means that coefficient estimates are not necessarily biased toward zero. Figure 1: Comparison of Data from Penn World Table Versions 6.1 (2002) and 7.1 (2012) 22

23 Table 1: Cases Where Revisions in Growth Exceeded ± 25 Percentage Points Country Year Old Growth Rate Current Growth Rate Difference Haiti Haiti Mali Nicaragua Rwanda Sierra Leone Togo Togo Uganda All values measured in percentage points. Old growth rate data from Penn World Table version 6.1, current data from version 7.1. It is beyond the scope of this paper to look more closely at these revisions. To be clear, there is no a priori reason to believe that the revisions in output growth correlate with revisions in other variables; the extent to which this is the case will be intimated by the comparison between Pollin s and Zhu s findings and the updated ones here. I make two key assumptions regarding the data. I assume that the revisions brought the data more closely in line with their true values. Additionally, I infer from their large prior revisions that the data are less reliable for middle- and low-income countries. For this reason, I will make few conclusions from the regressions on these data. To summarize, there is substantial evidence to suspect the quality of the data. However, aside from limiting inferences from the least reliable countries, there are few ways in which this risk can be mitigated. Missing data and sample selection bias are also of concern to this study. The dataset is not complete; there are numerous observations that do not have data for at least one variable. It is unlikely that such missing observations are randomly distributed across 23

24 countries and time. Attempts were made to include as much data as possible, while keeping the information used as current as possible. In particular, additional sources were used to obtain data for terms of trade and for government budget surpluses, as detailed in Appendix B. Ultimately, however, there were few alternative datasets that could be used to fill in the missing data. Regarding sample selection bias, the countries included in this study are quite diverse. However, there are three major sets of countries that appear to be systematically excluded from the dataset: former Soviet states and relatively new European states (e.g., a united Germany), oil-producing states, and relatively economically isolated countries (Cuba and North Korea, in particular). The unique phenomena associated with these countries provide a rationale for their exclusion from the dataset. As such, sample selection bias is not a major concern for this study. Lastly, simultaneous causality bias is of significant concern. It is a tacit assumption of the regression models that the input variables are exogenously determined. I have, in fact, consistently referred to them as independent variables. While convenient, this assumption is not particularly reasonable a priori. For example, businesses likely rely on recent years economic growth to gauge future activity. As such, economic growth in the past likely impacts investment decisions in the present. Additionally, inflation, too, may be endogenous with respect to growth. During a recession, policymakers may seek to use monetary stimulus to promote economic recovery. As such, the growth rate of the economy may influence the rate of inflation. In empirical studies, this concern is largely side-stepped. In Pollin and Zhu (2006), for example, discussion is relegated to a single footnote: they do not explore the issue of simultaneity or reverse causality in this exercise, although [they] recognize it as an important issue for further research (Pollin and Zhu, 2006: 603). It is difficult 24

25 to properly test for simultaneous causality. In particular, the limited time periods available for examination prevent the use of most conventional analyses on causality. While an instrumented variables regression would be able to account for some of the endogeneity, the approach is not readily applicable to this case. It is necessary to have at least as many instruments as there are endogenous variables. Both inflation and squared inflation would be endogenous to growth; finding a second instrument is not inherently straightforward. Presumably, this is why Pollin and Zhu (2006) chose to leave this question for future studies. It is also possible that simultaneous causality is most prevalent across the shortterm. Over longer periods of time, the variables may be exogenous with respect to one another. To the best of my knowledge, this assertion has not been explicitly tested for the variables used here, though there is some theoretical appeal to it. For example, while output-induced factors, such as demand pull and cost push, may impact the rate of inflation, such influences are thought to be negligible beyond the short-term McConnell, Brue, and Flynn (2012). Ultimately, limited availability of data prevents a more rigorous examination of the risk of simultaneous causality, so, following Pollin and Zhu (2006), this potential bias is not tested here. However, based on my belief that such bias is most likely in the short-term, I do not rely on the results from the decade regressions to determine my overall conclusions. As these regressions still provide an opportunity to compare the work done here with that of Pollin and Zhu (2006), they are still of use. Regarding the external validity of the data, there are two main questions: are the conclusions relevant to countries not included in the dataset and will these conclusions reflect reality in the future? It is very likely that the findings presented here are consistent with the experiences of many of the countries not included in the model. Modern Germany, for 25

26 example, would likely behave in a similar manner to the OECD countries included here. This study is unlikely, however to be effective in describing the growth of non-businessoriented economies. Command economies, oil states, and agrarian societies have unique structures that are beyond the focus here. Additionally, recall that all observations with rates of inflation beyond 40 percent are excluded from this analysis. As such, the inferences made from this analysis are constrained from properly examining economies during periods of hyperinflation. Burdekin et al. (2004), among others, suggest that the relationship between inflation and growth differs above this threshold. As such, while the exclusion of these observations from this analysis restricts the potential scope of the conclusions, it also reduces the risk of skewing the estimates by excluding outlier observations. For this reason, the benefits of this choice likely outweigh the costs. The consistency of my findings across time is perhaps the most pertinent question. In particular, is there a structural break in the relationship between one of the independent variables and growth? This model assumes that the true relationships between the independent variables and growth are constant over the period examined. This is an assumption made out of necessity rather than statistical evidence. With regard to inflation in particular, this belief is undermined by countries that have adopted inflation targeting for their monetary policy. This monetarist approach stabilizes inflation about a particular value, such that the rate of inflation is supposed to hold steady even as the economy moves through the business cycle. To the extent that central banks are able to achieve their targets, inflation should be unable to describe the variation in growth, even though it may have been able to do so in the past. If this phenomenon is present in the dataset used here, the current models will be undermined by not accounting for this. If a broader time period was available, there are several time series analyses that could be used to test for 26

27 the presence of a structural break. However, the limited availability of data undermines my ability to properly address this concern. To summarize this section, there are numerous sources of potential bias that may impact the regression model used here. Some of these, such as omitted variable bias, can be addressed, at least in part. However, there are others, such as simultaneous casualty and structural breaks, that are impossible to control for at this time. Unfortunately, the only recourse for a proper discussion of these sources of error is to wait for more data to become available. With a sufficiently long period of time available for analysis, econometric tests can be used to determine if these potential sources of error bias the model. In the meantime, the only way I can counter this error is to qualify my conclusions. 4 Results Here I present the outcomes of the regression analysis and compare them with the findings of Pollin and Zhu (2006). I start by examining the results of the decade analysis, shift to looking at the medium-term results, 4 and propose an augmented model which can be used to relate the Pollin and Zhu framework with the Mankiw, Romer, and Weil (1992) empirical model. Lastly, this augmented model is examined through the twenty-five year averages used by Mankiw, Romer, and Weil. There are two main goals here: test the validity of the Pollin and Zhu (2006) model and compare this model with that of Mankiw, Romer, and Weil (1992). As these models come from very different theoretical perspectives, this comparison should provide some intriguing insights. The primary way in which I compare Pollin s and Zhu s published findings with my own 4 Pollin and Zhu refer to these as long-term results. However, to keep the discussion in this paper clear, five-year averages will be referred to as medium-term. 27